A wireless network distributed average consensus method based on a graph neural network

Abstract

This invention relates to the field of wireless communication technology and discloses a distributed average consensus method for wireless networks based on graph neural networks. The method includes: establishing an undirected connected graph based on the wireless network and determining the arithmetic mean of the initial state values ​​of all nodes in the undirected connected graph; setting a consensus objective, wherein the final state values ​​of all nodes converge to the arithmetic mean; calculating the number of communication slots required to achieve the consensus objective; establishing an optimization problem with the objective of minimizing the number of communication slots; constructing and training a message passing neural network based on the graph neural network to obtain the final embedding vector of each node, and using the embedding vector to obtain the broadcast probability of each node; solving the optimization problem using the broadcast probability of each node to obtain the optimal slot, and achieving the consensus objective using a distributed linear iterative method based on the broadcast probability. This invention can improve consensus efficiency and reduce communication costs.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a distributed average consensus method for wireless networks based on graph neural networks. Background Technology

[0002] The goal of distributed average consensus is to enable all nodes in a network to converge to the arithmetic mean of their initial state values ​​through iterative communication. With the rapid development of emerging technologies such as unmanned aerial vehicle swarm control, decentralized federated learning, and data fusion, the demand for efficient and low-latency wireless communication is increasing. However, traditional wireless networks face numerous challenges in achieving distributed average consensus, primarily in terms of signal interference, network congestion, and energy limitations. Therefore, optimizing distributed average consensus algorithms in wireless networks is particularly important.

[0003] Existing average consensus algorithms typically employ linear iterative methods, which are popular due to their simplicity and scalability. However, they have limitations in ensuring fast convergence and reducing communication overhead. To address these issues, researchers have proposed several improved methods, such as hybrid matrix optimization based on semidefinite programming and consensus schemes that consider the randomness of network topology. However, these methods face problems of high communication costs and low efficiency in practical applications. Summary of the Invention

[0004] The primary objective of this invention is to overcome the problems existing in the prior art and provide a distributed average consensus method for wireless networks based on graph neural networks. This invention can improve consensus efficiency and reduce communication costs.

[0005] To achieve the above objectives, this invention provides a distributed average consensus method for wireless networks based on graph neural networks, comprising:

[0006] An undirected connected graph is established based on the wireless network, and the arithmetic mean of the initial state values ​​of all nodes in the undirected connected graph is determined.

[0007] Set a consensus objective, which is that the final state values ​​of all nodes converge to the arithmetic mean.

[0008] Calculate the number of communication slots required to achieve the consensus objective;

[0009] An optimization problem is established with the objective of minimizing the number of communication time slots;

[0010] Construct and train a message passing neural network based on a graph neural network to obtain the final embedding vector of each node, and use the embedding vector to obtain the broadcast probability of each node;

[0011] The optimization problem is solved using the broadcast probability of each node to obtain the optimal time slot, and the consensus objective is achieved using a distributed linear iterative method based on the broadcast probability.

[0012] Furthermore, the consensus objective is determined by the following formula:

[0013] 1 T x(0)

[0014] in, This represents the number of nodes in the wireless network. For nodes, , For the first The initial state values ​​of each node.

[0015] Furthermore, the number of communication slots required to achieve the consensus goal is calculated as follows:

[0016]

[0017] in, The expected error tolerance for consensus. , For the first The random mixing matrix in the consensus step.

[0018] Furthermore, the optimization problem is as follows:

[0019]

[0020] in, K is the average number of nodes scheduled to broadcast in each consensus step.

[0021] This represents the minimum scheduling probability for all nodes.

[0022] Furthermore, the construction and training of the message-passing neural network based on the graph neural network to obtain the final embedding vector of each node, and the use of the embedding vector to obtain the broadcast probability of each node, specifically includes:

[0023] (1). Establish a message passing neural network, which includes a message passing phase, an aggregation phase and an update phase;

[0024] (2). Iteratively train the message passing neural network to obtain the final graph embedding of each node;

[0025] (3). Embed the final graph of each node into the rescale function, specifically:

[0026]

[0027] Obtain the broadcast probability for each node.

[0028] Furthermore, iteratively training the message-passing neural network specifically includes:

[0029] (1). In each training session, during the message passing phase, each node generates a first message based on local features and edge features of neighboring nodes, and passes the first message to neighboring nodes. The local features are at least one of initial state value, node degree, PageRank value and betweenness centrality, and the edge features are at least one of strength, bandwidth and distance between nodes. During the aggregation phase, each node aggregates the first messages from all neighbors to generate a second message. During the update phase, each node updates its own node features based on the second message and local features. The node features of each node after the previous training session are used as local features for the next training session.

[0030] (2) Repeat the above operation until the above message passing neural network converges and the final graph embedding of each node is obtained.

[0031] Furthermore, the loss function used for iteratively training the message-passing neural network is as follows:

[0032]

[0033] in, , For the number of nodes, This refers to the size of a small batch.

[0034] Furthermore, the optimization problem is solved using the broadcast probability of each node to obtain the optimal time slot, including:

[0035] (1). The optimization problem is restated based on the monotonicity of the logarithmic function, as follows:

[0036]

[0037] in, , ;

[0038] (2). Input the broadcast probability of each node into the above formula to obtain the optimal time slot.

[0039] Furthermore, the consensus objective is achieved using a distributed linear iterative method based on the broadcast probability, specifically including:

[0040] (1). In each iteration step, each node determines whether to send its current state value to its neighboring nodes based on the broadcast probability, and the determination is specifically represented by a Bernoulli random variable:

[0041]

[0042] when At that time, node The status value is broadcast to all neighboring nodes. ,node No broadcasting will be conducted;

[0043] (2). Each node updates its state value by using a linear weighted average based on its current state value and the received state values ​​of its neighbors;

[0044] (3) Repeat the above steps until the consensus goal is achieved.

[0045] Furthermore, each node broadcasts its current state value to its neighboring nodes using Time Division Multiple Access (TDMA) and / or Orthogonal Frequency Division Multiple Access (OFDMA).

[0046] Compared with the prior art, the advantages of this invention are as follows:

[0047] This invention improves consensus efficiency in wireless networks and effectively reduces communication costs by using graph neural networks to dynamically adjust broadcast probabilities based on wireless network topology and node importance. Attached Figure Description

[0048] Figure 1 This is a flowchart of a distributed average consensus method for wireless networks based on graph neural networks, as described in Example 1.

[0049] Figure 2 This is a structural diagram of the neural network in Example 1;

[0050] Figure 3 This is a diagram of the message passing neural network framework for Example 1;

[0051] Figure 4 This is the convergence of the graph neural network in Example 2 with different numbers of nodes;

[0052] Figure 5 This is a comparison diagram of the neural network and other broadcasting methods in Example 2 at different network sizes;

[0053] Figure 6 This is a performance comparison diagram of the neural network and other broadcast methods in Example 2 when the network size is the same but the K value is different;

[0054] Figure 7This is a graph comparing the root mean square error performance of the neural network and other broadcast methods in the entire consensus process, as shown in Example 2. Detailed Implementation

[0055] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0056] In the description of this invention, it should be noted that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0057] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0058] Furthermore, in the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0059] Example 1

[0060] like Figure 1 As shown, a preferred embodiment of the present invention provides a distributed average consensus method for wireless networks based on graph neural networks, comprising:

[0061] S1: Construct an undirected connected graph based on the wireless network, and determine the arithmetic mean of the initial state values ​​of all nodes in the undirected connected graph;

[0062] In one embodiment, consider a containing A wireless network with [number] nodes. This wireless network is represented as an undirected connected graph. ,in Represents a set of nodes. Represents the set of edges. Edges Indicates the first The node can directly connect with the first node. Individual node communication. Graph connectivity can also be determined using an adjacency matrix. To describe, where if and There is a connection (i.e.) ),but for Otherwise .set up Represents a node The set of neighbors. Node The degree is defined as ,Right now No. The sum of row elements can also be expressed as ,in The cardinality of a set is represented by . The degree matrix is ​​denoted as . It is a diagonal matrix, where the diagonal elements are the degrees of each node, i.e. The Laplace matrix is ​​denoted as... Through the degree matrix Subtract the adjacency matrix To obtain, that is .

[0063] The initial state value of a node represents the state of the node at the start of consensus. Optionally, the initial state value can be the data value or signal value held by the node.

[0064] S2: Set a consensus objective, which is that the final state values ​​of all nodes converge to the arithmetic mean.

[0065] In one embodiment, the consensus objective is as follows:

[0066]

[0067] in , Indicates the first The initial state values ​​of each node. To achieve this goal, the following distributed linear iterative method is used:

[0068]

[0069] in Indicates the index of the consensus steps. It is the first Step in the first The state values ​​of each node. Indicates assignment to the first The node is the _th The weights assigned to the state values ​​of each node. The meaning is: node When updating its state value, it takes into account both its own current state value and the current state values ​​of all its neighboring nodes. Weight Represents a node The impact on its own state value, and the weights Represents a node Its neighboring nodes The degree to which the state value of each neighboring node depends on the node's state value. These weights determine the degree to which the state value of each neighboring node depends on the node's state value. The proportion of time allocated to state updates affects the convergence speed and stability of the consensus algorithm throughout the network. The distributed linear iterative method can be more concisely represented as:

[0070]

[0071] in Weight matrix Also known as a hybrid matrix. Because not all nodes can communicate directly, a hybrid matrix... The network must adhere to sparse pattern constraints based on its connectivity, namely:

[0072]

[0073] Given any initial state value and with a fixed weight matrix In iterative mixing, the final state value of each node is expected to converge to the arithmetic mean of its initial state values, i.e.:

[0074]

[0075] in The above is also equivalent to:

[0076]

[0077] According to this formula, it holds if and only if the following conditions are met:

[0078]

[0079] A simple choice of mixing matrix is ,in , , The matrix represents the identity matrix. In the above formula, the spectral radius... Also known as the asymptotic convergence factor, it is closely related to the convergence speed of the average consensus process.

[0080] S3: Calculate the number of communication slots required to achieve the consensus goal;

[0081] In one embodiment, the number of steps required for the consensus process to converge can be estimated as follows:

[0082]

[0083] in This represents the expected error tolerance for consensus. Given that wireless networks have... Each node requires [number] consensus steps. This process is completed in one communication time slot. Therefore, the entire consensus process in a wireless network requires... One communication time slot.

[0084] To reduce communication costs, this embodiment proposes a probabilistic broadcast scheme. In this scheme, only a subset of nodes are scheduled to broadcast information to their neighbors during each consensus step. The broadcast probability of each node is denoted as . ,satisfy ,in It is predefined, and This means that on average, about [number missing] people participate in each consensus step. Each node is scheduled to broadcast. For this probabilistic broadcast scheme, the number of steps required for the consensus process to converge can be estimated as follows:

[0085]

[0086] in Indicates the first The elements of the random mixing matrix in the consensus step are defined as follows:

[0087]

[0088] In the above formula, It is a Bernoulli random variable with probability Values ,Right now Indicates the first The node at the th In the consensus process, if selected to broadcast, otherwise... It should be mentioned that, in order to ensure The randomness of the rows necessitates adjustments to the diagonal elements. Therefore, The elements can be represented as:

[0089]

[0090] S4: Establish an optimization problem with the objective of minimizing the number of communication time slots;

[0091] In one embodiment, a method for numerically optimizing the broadcast probability vector is proposed. The goal is to minimize the number of communication slots required to achieve average consensus in a wireless network. The optimization problem can be formulated as:

[0092]

[0093] Within constraints, This represents the minimum scheduling probability for all nodes. This value is set to prevent the broadcast probability from reaching zero. This is necessary because if some nodes have a zero broadcast probability, they will not be scheduled to broadcast their values ​​to their neighbors during the consensus process, thus preventing the network from achieving average consensus.

[0094] S5: Construct and train a message passing neural network based on a graph neural network to obtain the final embedding vector of each node, and use the embedding vector to obtain the broadcast probability of each node;

[0095] In one embodiment, S5 specifically includes:

[0096] (1) Establish a message passing neural network, which includes a message passing phase, an aggregation phase, and an update phase. Figure 2 This is a diagram of the structure of a graph neural network. Figure 3 This is a diagram of a message passing neural network framework;

[0097] (2). Iteratively train the message passing neural network to obtain the final graph embedding of each node;

[0098] (3). Embed the final graph of each node into the rescale function, specifically:

[0099]

[0100] Obtain the broadcast probability for each node.

[0101] It should be noted that iterative training of the message-passing neural network specifically includes:

[0102] (1). In each training iteration, during the message passing phase, each node generates a first message based on its local features and the edge features of its neighboring nodes, and passes the first message to its neighboring nodes. The local features are at least one of the initial state value, node degree, PageRank value, and betweenness centrality; the edge features are at least one of the strength, bandwidth, and distance between nodes. During the aggregation phase, each node aggregates the first messages from all its neighbors to generate a second message. During the update phase, each node updates its own node features based on the second message and its local features. The node features of each node after the previous training iteration are used as local features for the next training iteration. Formally, the message passing, aggregation, and update phases of the MPNN framework can be represented as follows:

[0103]

[0104] The first in GNN In the layer, From the first The node to the first Messages generated by each node; It is the first Graph embedding of nodes, It comes from the first Aggregated messages from the neighboring nodes of each node; and All are GNN number Characteristics of the layer. The function is They possess substitutional variability, thus The output does not change regardless of the order of the input messages. Message functions for all nodes in the graph. and update function They each have parameters and The multilayer perceptron (MLP), after N rounds of updates, utilizes each node The final embedding determines the broadcast probability of network nodes, see details. Figure 2 Diagram of a message passing neural network framework.

[0105] The proposed learning algorithm is trained offline in an unsupervised manner using mini-batch samples, where the training data is uniformly sampled from the training set. This yields the final embedding for each node. Then, the rescale function is used to make... The specific expression is:

[0106]

[0107] in It is a scaling factor that makes , and These represent the minimum and maximum values ​​of the broadcast probability, respectively.

[0108] (2) Repeat the above operation until the above message passing neural network converges and the final graph embedding of each node is obtained.

[0109] Furthermore, the loss function used for iteratively training the message-passing neural network is as follows:

[0110]

[0111] in, , For the number of nodes, By using a small batch size, the loss function can directly link the optimization of broadcast probability with the improvement of consensus speed, achieving the goal of rapid average consensus among distributed nodes. By optimizing this loss function using gradient descent, the model in this study can learn how to dynamically adjust the broadcast probability based on the network structure and node characteristics to optimize the communication efficiency of the entire wireless network.

[0112] S6: Solve the optimization problem using the broadcast probability of each node to obtain the optimal time slot, and achieve the consensus goal using a distributed linear iterative method based on the broadcast probability.

[0113] In one embodiment, solving the optimization problem using the broadcast probability of each node to obtain the optimal time slot includes:

[0114] (1). The optimization problem is restated based on the monotonicity of the logarithmic function, as follows:

[0115]

[0116] in, , ;

[0117] (2). Input the broadcast probability of each node into the above formula to obtain the optimal time slot.

[0118] Achieving consensus goals using a distributed linear iterative method based on broadcast probability includes:

[0119] (1). In each iteration step, each node determines whether to send its current state value to its neighboring nodes based on the broadcast probability, and the determination is specifically represented by a Bernoulli random variable:

[0120]

[0121] when At that time, node The status value is broadcast to all neighboring nodes. ,node No broadcasting is performed; to effectively implement the above consensus algorithm in a wireless network, leveraging the broadcast characteristics of the wireless medium, several key factors need to be considered. In each consensus step, each node... It needs to be obtained from its neighboring nodes. Collect numerical values ​​and use a blending matrix The The row updates its own value, as described in the distributed linear iterative method, for To ensure that nodes do not interfere with each other, a feasible approach is to schedule nodes to broadcast information to their neighbors using orthogonal multiple access schemes (such as time division multiple access (TDMA) or orthogonal frequency division multiple access). This embodiment considers the TDMA strategy without loss of generality. By adopting this strategy, each node can broadcast information to its neighbors without interfering with other nodes.

[0122] (2). Each node updates its state value using a linear weighted average based on its current state value and the received state values ​​of its neighbors. The linear weighted average method is as follows:

[0123]

[0124] (3) Repeat the above steps until the consensus goal is achieved, namely:

[0125] .

[0126] This embodiment improves consensus efficiency in wireless networks and effectively reduces communication costs by using graph neural networks to dynamically adjust broadcast probabilities based on wireless network topology and node importance.

[0127] Example 2

[0128] To evaluate the performance of graph neural network (GNN) based methods, the following baseline algorithms are proposed for comparative experiments. In the experimental simulation, all graphs are used... The graph is generated randomly. The edges between any two nodes in the graph are... The probability is established. The mixing matrix is ​​set as follows: ,in The minimum broadcast probability for all nodes is set to For each training iteration, the gradient of the loss function is estimated in an unsupervised manner using a batch of 50 samples. The parameters of the GNN-based model are updated using the ADAM algorithm with a learning rate of 0.001. The dimension of the graph embedding for each node is set to 16. The number of convolutional layers in the GNN is set to 3.

[0129] 1. Use the node's PageRank value, degree, and betweenness centrality as methods for broadcasting probability.

[0130] Figure 4 The convergence behavior of the proposed GNN method is illustrated, and the performance of the framework considered during training is described. For comparison, this embodiment also shows the convergence for N=50, N=40, and N=30, where K=0.8*K, as shown below. Figure 4As shown, when N=30, the network tends to converge in the 6th epoch, and the others converge within the 10th epoch.

[0131] exist Figure 5 In this study, training was considered on networks with N = 50 and K = 40. After training, these policies were frozen, i.e., their parameters were kept constant, demonstrating the effectiveness of the proposed GNN method in different scenarios. Value The network was evaluated, and it can be seen that among the methods that directly use the PageRank value, degree, and betweenness centrality of nodes as broadcast probabilities, the method that uses betweenness centrality as broadcast probability is the best. Therefore, we choose betweenness centrality as the feature of GNN nodes, but the proposed GNN method is better than the other three methods.

[0132] exist Figure 6 In this case, we considered the case where N=30 and K takes different values. The performance of training on the network shows that the proposed GNN method is superior to the other three methods. Note that when N=30 and K=30, the probability of all nodes is 1, so the performance of the four methods is the same.

[0133] 2. In addition to optimizing the broadcast probability, the following metrics were used to further evaluate the performance of the GNN method.

[0134] The average number of iterations required for the consensus process to converge; the total number of communication time slots required to reach consensus; and the root mean square error between the state values ​​of all nodes and the average value in each consensus step.

[0135] like Figure 7 As shown, this paper compares the root mean square error (RMSE) performance of different schemes throughout the consensus process. and Due to the time-varying mixing matrix It is row-random rather than double-random, so although all nodes can reach a consensus, the final state value may not be the average of the initial state values. To solve this problem, a bias correction method based on pre-compensation is adopted. In the... In this consensus step, RMSE can be calculated as follows: or In the diagram, "unscheduled" means that all nodes are scheduled to broadcast information to their neighbors in each consensus step, i.e. .from Figure 7 As can be seen, the proposed solution outperforms other benchmark solutions by a significant margin. This underscores the importance of optimizing broadcast probabilities and highlights the effectiveness of the solution proposed in Example 1.

[0136] In summary, this invention provides a distributed average consensus method for wireless networks based on graph neural networks. By using graph neural networks to dynamically adjust the broadcast probability according to the wireless network topology and node importance, it improves the consensus efficiency in wireless networks and effectively reduces communication costs.

[0137] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and substitutions can be made without departing from the technical principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention.

Claims

1. A distributed average consensus method for wireless networks based on graph neural networks, characterized in that, The method includes the following steps: An undirected connected graph is established based on the wireless network, and the arithmetic mean of the initial state values ​​of all nodes in the undirected connected graph is determined. Set a consensus objective, which is that the final state values ​​of all nodes converge to the arithmetic mean. Calculate the number of communication slots required to achieve the consensus objective; An optimization problem is established with the objective of minimizing the number of communication time slots; Construct and train a message passing neural network based on a graph neural network to obtain the final embedding vector of each node, and use the embedding vector to obtain the broadcast probability of each node; The optimization problem is solved using the broadcast probability of each node to obtain the optimal time slot, and the consensus objective is achieved using a distributed linear iterative method based on the broadcast probability.

2. The distributed average consensus method for wireless networks based on graph neural networks according to claim 1, characterized in that, The consensus objective is determined by the following formula: 1 T x(0) in, This represents the number of nodes in the wireless network. For nodes, , For the first The initial state values ​​of each node.

3. The distributed average consensus method for wireless networks based on graph neural networks according to claim 2, characterized in that, The number of communication slots required to achieve the consensus goal is calculated as follows: in, The expected error tolerance for consensus. , For the first The random mixing matrix in the consensus step.

4. The distributed average consensus method for wireless networks based on graph neural networks according to claim 3, characterized in that, The optimization problem is as follows: in, K is the average number of nodes scheduled to broadcast in each consensus step. This represents the minimum scheduling probability for all nodes.

5. The distributed average consensus method for wireless networks based on graph neural networks according to claim 4, characterized in that, The construction and training of the message passing neural network based on the graph neural network to obtain the final embedding vector of each node, and the use of the embedding vector to obtain the broadcast probability of each node, specifically includes: (1). Establish a message passing neural network, which includes a message passing phase, an aggregation phase and an update phase; (2). Iteratively train the message passing neural network to obtain the final graph embedding of each node; (3). Embed the final graph of each node into the rescale function, specifically: Obtain the broadcast probability for each node.

6. A distributed average consensus method for wireless networks based on graph neural networks as described in claim 5. The method, characterized in that, Iterative training of the message-passing neural network specifically includes: (1). In each training session, during the message passing phase, each node generates a first message based on local features and edge features of neighboring nodes, and passes the first message to neighboring nodes. The local features are at least one of initial state value, node degree, PageRank value and betweenness centrality, and the edge features are at least one of strength, bandwidth and distance between nodes. During the aggregation phase, each node aggregates the first messages from all neighbors to generate a second message. During the update phase, each node updates its own node features based on the second message and local features. The node features of each node after the previous training session are used as local features for the next training session. (2) Repeat the above operation until the above message passing neural network converges and the final graph embedding of each node is obtained.

7. A distributed average consensus method for wireless networks based on graph neural networks as described in claim 6. The method is characterized by, The loss function used for iterative training of the message-passing neural network is as follows: in, , For the number of nodes, This refers to the size of a small batch.

8. A distributed average consensus method for wireless networks based on graph neural networks as described in claim 6 The method, characterized in that, The optimization problem is solved using the broadcast probability of each node to obtain the optimal time slot, including: (1). The optimization problem is restated based on the monotonicity of the logarithmic function, as follows: in, , ; (2). Input the broadcast probability of each node into the above formula to obtain the optimal time slot.

9. A distributed average consensus method for wireless networks based on graph neural networks as described in claim 1 The method, characterized in that, The consensus objective is achieved using a distributed linear iterative method based on the broadcast probability, specifically including: (1). In each iteration step, each node determines whether to send its current state value to its neighboring nodes based on the broadcast probability, and the determination is specifically represented by a Bernoulli random variable: when At that time, node The status value is broadcast to all neighboring nodes. ,node No broadcasting will be conducted; (2). Each node updates its state value by using a linear weighted average based on its current state value and the received state values ​​of its neighbors; (3) Repeat the above steps until the consensus goal is achieved.

10. A distributed average consensus method for wireless networks based on graph neural networks according to claim 9, characterized in that, The communication method adopted by each node to broadcast its current state value to its neighboring nodes is time division multiple access and / or orthogonal frequency division multiple access.

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